Cores in random hypergraphs and Boolean formulas

Authors:
Michael Molloy
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4 and Microsoft Research, Redmond, Washington
Venue:
Random Structures & Algorithms
Year:
2005

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Abstract

We describe a technique for determining the thresholds for the appearance of cores in random structures. We use it to determine (i) the threshold for the appearance of a k-core in a random r-uniform hypergraph for all r, k ≥ 2, r + k 4, and (ii) the threshold for the pure literal rule to find a satisfying assignment for a random instance of r-SAT, r ≥ 3. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005